Skip to main content
Springer Nature Link
Log in

Meshing complexity: predicting meshing difficulty for single part CAD models

  • Special Issue
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

This paper proposes a method for predicting the complexity of meshing computer aided design (CAD) geometries with unstructured, hexahedral, finite elements. Meshing complexity refers to the relative level of effort required to generate a valid finite element mesh on a given CAD geometry. A function is proposed to approximate the meshing complexity for single part CAD models. The function is dependent on a user defined element size as well as on data extracted from the geometry and topology of the CAD part. Several geometry and topology measures are proposed, which both characterize the shape of the CAD part and detect configurations that complicate mesh generation. Based on a test suite of CAD models, the function is demonstrated to be accurate within a certain range of error. The solution proposed here is intended to provide managers and users of meshing software a method of predicting the difficulty in meshing a CAD model. This will enable them to make decisions about model simplification and analysis approaches prior to mesh generation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Butlin G, Stops C (1996) CAD data repair. In: Proceedings of 5th international meshing roundtable, pp 7–12

  2. Cheney D (1998) CAD model quality holds the key for analysis. In: Proceedings 7th International Meshing Roundtable, pp 539–546

  3. Mezentsev A (1999) Methods and Algorithms of Automated CAD Repair for Incremental Surface Meshing. Proceedings 8th International Meshing Roundtable, pp 299–309

  4. http://www.spatial.com, April 2003

  5. http://www.eds.com/products/plm/parasolid/portfolio/bodyshop.shtml, April 2003

  6. http://www.cadfix.com, April 2003

  7. http://www.cadiq.com, April 2003

  8. White D, Leland R, Saigal S, Owen S (2001) The meshing complexity of a solid: an introduction. In: Proceedings of 10th International meshing roundtable, pp 373–384

  9. Steinbrenner J, Wyman N, Chawner J (2000) Fast surface meshing on imperfect cad models. In: Proceedings 9th International meshing roundtable. pp 33–41

  10. Marcum D, Gaither A (1999) Unstructured surface grid generation using global mapping and physical space approximation. In: Proceedings 8th International meshing roundtable, pp 397–406

  11. Sheffer A, Blacker T, Clements J, Bercovier M (1997) Virtual topology operators for meshing. In: Proceedings 6th International meshing roundtable, pp 49–66

  12. Sheffer A, Blacker T, Bercovier M (1997) Clustering: automated detail suppression using virtual topology. Trends in unstructured mesh generation. ASME 220:57–64

    Google Scholar 

  13. Armstrong C, Bridgett S, Donaghy R, McCune R, McKeag R, Robinson D (1998) Techniques for interactive and automatic idealisation of CAD models. Num Grid Generation Comp Field Sim, pp 643–662

  14. Blacker T, Sheffer A, Clements J, Bercovier M (1997) Using virtual topology to simplify the mesh generation process. Trends in unstructured mesh generation. ASME 200:45–50

    Google Scholar 

  15. Tautges T (2001) Automatic detail reduction for mesh generation applications. In: Proceedings 10th International meshing roundtable, pp 407–418

  16. Mobley A, Carroll M, Canann S (1998) An object oriented approach to geometry defeaturing for finite element meshing. In: Proceedings 7th International meshing roundtable, pp 547–563

  17. Armstrong C, Robinson D, McKeag R, Li T, Bridgett S, Donaghy R, McGleenan C (1995) Medials for meshing and more. In: Proceedings 4th International meshing roundtable, pp 277–288

  18. Sheffer A, Etzion M, Rappoport A, Bercovier M (1998) Hexahedral mesh generation using the embedded voronoi graph. In: Proceedings 7th International meshing roundtable, pp 347–364

  19. Lu Y, Gadh R, Tautges TJ (1999) Volume decomposition and feature recognition for hexahedral mesh generation. In: Proceedings 8th International meshing roundtable, pp 269–280

  20. Schneiders R, Schindler R, Weiler F (1996) Octree-based generation of hexahedral element meshes. In: Proceedings 5th International roundtable pp 205–216

  21. Tautges T, Blacker T, Mitchell S (1996) The whisker weaving algorithm: a connectivity-based method for constructing all-hexahedral finite element meshes. Int J Num Methods Eng 39:3327–3349

    Article  MATH  MathSciNet  Google Scholar 

  22. Folwell N, Mitchell S (1998) Reliable whisker weaving via curve contraction. In: Proceedings 7th International meshing roundtable, pp 365–378

  23. Blacker T, Meyers R (1993) Seams and wedges in plastering: a 3D hexahedral mesh generation algorithm. Eng Comput 2:83–93

    Article  Google Scholar 

  24. Mitchell S (1998) The all-hex geode-template for conforming a diced tetrahedral mesh to any diced hexahedral mesh. In: Proceedings 7th International meshing roundtable, pp 295–305

  25. Muller- Hannemann M (1998) Hexahedral mesh generation by successive dual cycle elimination. In: Proceedings 7th International meshing roundtable, pp 365–378

  26. Ymakawa S, Shimada K (2001) Hexhoop: modular templates for converting a hex-dominant mesh to an all-hex mesh. In: Proceedings 10th International meshing roundtable, pp 235–246

  27. Cook W, Oaks W (1983) Mapping methods for generating three-dimensional meshing. Comput Mech Eng 1:67–72

    Google Scholar 

  28. White D, Mingwu L, Benzley S, Sjaardema G (1995) Automated hexahedral mesh generation by virtual decomposition. In: Proceedings 4th International meshing roundtable, pp 165–176

  29. Blacker T (1996) The cooper tool. In: Proceedings 5th International meshing roundtable, pp 13–30

  30. White D, Tautges T (2000) Automatic scheme selection for toolkit hex meshing. Int J Num Methods Eng 49:127–144

    Article  MATH  Google Scholar 

  31. Mitchell S (1997) High fidelity interval assignment. In: Proceedings 6th International meshing roundtable, pp 33–44

  32. Tautges T (2000) The common geometry module (CGM): a generic, extensible geometry interface. In: Proceedings 9th International meshing roundtable 337–348

  33. Blacker T (1991) Paving: a new approach to automated quadrilateral mesh generation. Int J Num Methods Eng 32:811–847

    Article  MATH  Google Scholar 

  34. Owen S, Staten M, Canann S, Saigal S (1999) Q-Morph: an indirect approach to advancing front quad meshing. Int J Num Methods Eng 44:1317–1340

    Article  MATH  Google Scholar 

  35. Mitchell S (1997) Choosing corners of rectangles for mapped meshing. In: 13th Annual symposium on computational geometry, ACM Press, pp 87–93

  36. Shepherd J (2003) CUBIT mesh generation toolsuite. http://cubit.sandia.gov.

Download references

Acknowledgements

The authors wish to acknowledge Sandia National Laboratories for providing funding and motivation for this project. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94-AL85000. Additionally, we wish to thank ANSYS Inc. for providing many of the CAD models that were included in the test suite.

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    David R. White, Sunil Saigal & Steven J. Owen

  2. Sandia National Laboratories, PO Box 5800, MS 0847, Albuquerque, NM, 87185-0847, USA

    David R. White & Steven J. Owen

  3. Department of Civil and Environmental Engineering, University of South Florida, Tampa, FL, 33620-5350, USA

    Sunil Saigal

Authors
  1. David R. White
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Sunil Saigal
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Steven J. Owen
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to David R. White.

Rights and permissions

Reprints and permissions

About this article

Cite this article

White, D.R., Saigal, S. & Owen, S.J. Meshing complexity: predicting meshing difficulty for single part CAD models. Engineering with Computers 21, 76–90 (2005). https://doi.org/10.1007/s00366-005-0002-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-005-0002-x

Keywords